I think there is a mistake in the subject area. This has nothing to do with geography, but with physics. This topic is about the linear expansion of conductive materials when heated to a higher temperature. The equation for linear expansion is
ΔL = L0*α*ΔT, where
ΔL is the change in length when heated
L0 is the original length of the rod
α is the coefficient of linear expansion; this is an empirical data for a specific kind of material
ΔT is the change in temperature
Since ΔL is same for lead and quartz, we can equate them.
L0,lead*α,lead*ΔT = L0,quartz*α,quartz*ΔT
The α for lead is 29×10^6 °C/m while the α for quartz is 14×10^6 °C/m. Since ΔT are the same for both materials, ΔT will be cancelled out. Therefore, the equation for L0,quartz is:
L0,quartz = (L0,lead*α,lead)/α,quartz
L0,quartz = (0.10 m*29×10^6 °C/m)/14×10^6 °C/m
L0,quartz = 0.207 m
